Correlators for the Wigner-Smith time-delay matrix of chaotic cavities

Abstract

We study the Wigner-Smith time-delay matrix $Q$ of a ballistic quantum dot supporting $N$ scattering channels. We compute the $v$-point correlators of the power traces $\mathrm{Tr}{Q}^{\kappa }$ for arbitrary $v\ge 1$ at leading order for large $N$ using techniques from the random matrix theory approach to quantum chromodynamics. We conjecture that the cumulants of the $\mathrm{Tr}{Q}^{\kappa }$'s are integer-valued at leading order in $N$ and include a MATHEMATICA code that computes their generating functions recursively.

20 pages, 1 table. v2: Typos fixed

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Cited by in corpus (15)

• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Moments of random matrices and hypergeometric orthogonal polynomials
• Large $N$ expansions for the Laguerre and Jacobi $\beta$ ensembles from the loop equations
• Large-$N$ expansion for the time-delay matrix of ballistic chaotic cavities
• Moments of the eigenvalue densities and of the secular coefficients of $\beta$-ensembles
• Recursion for the smallest eigenvalue density of $\beta$-Wishart-Laguerre ensemble
• Integer moments of complex Wishart matrices and Hurwitz numbers
• Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts
• Truncated linear statistics associated with the eigenvalues of random matrices II. Partial sums over proper time delays for chaotic quantum dots
• Linear Differential Equations for the Resolvents of the Classical Matrix Ensembles
• Ergodic Decomposition for Inverse Wishart Measures on Infinite Positive-Definite Matrices
• Time delay statistics for finite number of channels in all symmetry classes
• Wigner-Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity
• Semiclassical approach to $S$ matrix energy correlations and time delay in chaotic systems
• Semiclassical calculation of time delay statistics in chaotic quantum scattering